The aim of this project is the development of statistical methods that either take into account interpixel correlation or apply global image transform methods that permit an unbiased decomposition of images into uncorrelated components. Three statistical methods have been developed based on the Fourier transform, the wavelet transform, and the theory of Gaussian random fields. In the Fourier domain, the statistics at different wave numbers are uncorrelated and statistical tests can be performed unencumbered by spatial correlations. This method yields relatively poor spatial localization, but provides for rigorous statistical testing. However, by taking into account image blurring constraints, localization may be significantly improved. Statistical tests performed on PET images from alcoholic and normal subjects identified approximately 150 wave numbers (out of 8000) as significantly (p less than .05) different between the groups. For the wavelet- transform based analysis, a mathematically rigorous theory has been established, providing for the use of well known parametric statistical tests on wavelet coefficients. By exploiting orthogonality and regularity conditions, a two-stage testing procedure has been developed that resulted in a substantial reduction of the number of required tests (and thus a smaller Bonferroni adjustment). For PET images, the search space was reduced to 5-8 percent, and for functional MRI to about 10 percent of the original space. In both modalities about 1 percent of the coefficients were found to express significant (p less than .05, per volume) functional change. PET image differences between baseline and stimulation by mCPP from 13 normal and 19 alcoholic subjects demonstrated strong increases of glucose utilization in the orbitofrontal cortex, the caudate nuclei, the anterior thalamus, and both anterior and posterior cingulate gyri in the normals, while alcoholics showed, in general, absence of significant responses. Application of Gaussian random field tests to the same PET data identified significant differences in generally the same regions as the wavelet method. Also, Gaussian random field analysis was able to demonstrate in alcoholics a significant negative correlation of the glucose utilization rate in the prefrontal cortex with the external variable age.